An Analytical Model of the Write Process in Digital Magnetic Recording

Medium magnetizations for longitudinal high-density digital recordings

“…Here, expression (40) of Middleton et al [1], with some changes to symbols, has been manipulated to represent the rolloff curve as where is the arctangent transition width parameter, is the remanent magnetization, is the head to medium spacing, is the medium thickness, is the replay head gap length, is the wavelength of recording, is the number of turns on the head which has efficiency , is the track width, is the medium velocity, and is the permeability of free space. The transition widths have, likewise, been predicted by many authors, but here the calculations of Middleton [2], originally carried out for very thin media, have been repeated with the restriction of the thin film approximation lifted and the result for a write limited transitions is (2a) where is the medium coercivity, is the slope of the hysteresis loop at the coercive field which is often given as [3], and is a factor introduced by Williams and Comstock [4] to account for the influence of head gap length and record current amplitude on head field gradient [3], [4]. has values less than or equal to unity, and for a narrow gap head receiving near to optimum record currents, as assumed here, the value is unity.…”

Switching times and transition widths in digital recording theory

“…Simple modifications can now be made to many of the earlier calculations of the transition widths in longitudinal recording especially those of Williams and Comstock [3]. Here a modification of the approach of Middleton [4] for thin films yields (9) where is the slope of the hysteresis loop of the recording medium at , is the remanent magnetization, and takes the value of the head to medium spacing , and is the thickness of the recording medium.…”

An analytical model of the vector digital magnetic recording process in isotropic thin media

“…To calculate a x and a y using the basic methodology of Williams and Comstock [7] it is necessary to solve (9a) and (9b) at the centre of the transition. Applying (9a) and (9b) in the usual way [1] in a thin medium leads to…”